Differential Equations

4

Differential Equations of the First Order but not of the First Degree

We will now discuss the solutions of differential equations which are of the first order but are of degree higher than one. Such differential equations will contain only the first order differential coefficient but will occur in a degree higher than one. It is usual to denote by p. The general form of such a differential equation is then

 

pⁿ + A₁ pⁿ⁻¹ + A₂ pⁿ⁻² + … + A_n−1 p + A_n = 0

 

where A₁, A₂ … A_n are some functions of x and y.

Now we will consider various methods of ...